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Differential Operators Having Symmetric Orthogonal Polynomials as Eigenfunctions by H. Bavinck; J. Koekoek is a Mathematics article available to read on EtoBox.

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Let the polynomials {P,(x)}n°~0, orthogonal with respect to a symmetric positive definite moment functional a, be eigenfunctions of a linear differential operator L. We consider the orthogonal polynomials {PA'(x)}~0 and {PA"~(x)}~0, which are obtained by adding one resp. two symmetric (Sobolev type) terms to a. In all the cases we derive a representation for the polynomials and show that they are eigenfunctions of one or more linear differential operators (mostly of infinite order) of the form L+pA resp. L+#A +vB+#vC. Further it is investigated to what extend the eigenvalues can be chosen arbitrarily and finally expressions are given for the other eigenvalues. (g

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Author

H. Bavinck; J. Koekoek

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0377-0427)

Published

1999

Language

EN

Field

Mathematics (Physical Sciences)